To address the problem (REF ), mean-field approximation [1]} is widely used to offer a tractable solution of (REF ), which assumes that the variational pdf can be represented in a fully factorized form, i.e., \(Q(\Theta )= \mathop \prod \limits _{j=1}^{J}Q({\Theta }_j)\) , where \({\Theta }_j\in \Theta \)  is part of \(\Theta \)  with \(\bigcup _{j=1}^{J}\Theta _j=\Theta \)  and \(\bigcap _{j=1}^{J}\Theta _j=\varnothing \) , and \(J\)  is the number of subsets. With this factorization, (REF ) reduces to
\(\mathop \mathrm {minimize} \limits _{Q(\lbrace {\Theta }_j\rbrace _{j=1}^J)}-\mathbb {E}_{\lbrace Q({\Theta }_j)\rbrace _{j=1}^J}\left\lbrace \ln \left(\frac{p(\Theta |\lbrace \mathcal {Y}_l\rbrace _{l=1}^L)}{\prod _{j=1}^{J}Q({\Theta }_j)}\right)\right\rbrace .\) 
